This type of test images are only a weak indication of actual image quality, they don't mirror real shots (with subjects at much larger distance, higher contrast/different lighting etc.).

distance, contrast or different lighting should have minimal impact to IQ comparison. the only noticeable comparison would be where lighting is lacking, 6D + 4-105 would then trump 7D + 15-85 by a huge margin.

Real life images show that you are wrong,

Real life images show I am right. I own 17-55 which is better than 15-85, I also own Nikon 24-85, which is on par with 24-85. I have shot thousands photos using both, difference is very visible.

Do you own them both?

By the way, I have also shot extensively using 24-105 which I do not own, while I do not normally advocate for this lens, when mounted on FF it is indeed superior than aps-c with any similar zoom.

at least regarding corner performance (I'm not interested in slightly better center performance if the corners are blurred, but YMMV).

Corrner performance is very close, neither is great. But since 15mmm F3.5 is more or less close to 24mm F5.6 on FF, 6D at 24mm f5.6 is indeed a lot better than 7D on 15mm F3.5.

P.S.: I'm a scientist, I have my own thoughts about 'mathematical certainties'

For someone who does not understand such basic principle, you must be a scientist of scientology.